The central authority that runs AACS (the anticopying/DRM system used on commercial HD-DVD and Blu-ray discs) announced [April 6, 2007 item] last week the reissue of some software players that can play the discs, “[i]n response to attacks against certain PC-based applications”. The affected applications include WinDVD and probably others.

Recall that analysts had previously extracted from software players a set of decryption keys sufficient to decrypt any disc sold thus far. The authority could have responded to these attacks by blacklisting the affected applications or their decryption keys, which would have limited the effect of the past attacks but would have rendered the affected applications unable to play discs, even for law-abiding customers – that’s too much collateral damage.

To reduce the harm to law-abiding customers, the authority apparently required the affected programs to issue free online updates, where the updates contain new software along with new decryptions keys. This way, customers who download the update will be able to keep playing discs, even though the the software’s old keys won’t work any more.

The attackers’ response is obvious: they’ll try to analyze the new software and extract the new keys. If the software updates changed only the decryption keys, the attackers could just repeat their previous analysis exactly, to get the new keys. To prevent this, the updates will have to restructure the software significantly, in the hope that the attackers will have to start their analysis from scratch.

The need to restructure the software explains why several months expired between the attacks and this response. New keys can be issued quickly, but restructuring software takes time. The studios reportedly postponed some planned disc releases to wait for the software reissue.

It seems inevitable that the attackers will succeed, within a month or so, in extracting keys from the new software. Even if the guts of the new software are totally unlike the old, this time the attackers will be better organized and will know more about how AACS works and how implementations tend to store and manage keys. In short, the attackers’ advantage will be greater than it was last time.

When the attackers manage to extract the new keys, a new round of the game will start. The player software will have to be restructured again so that a new version with new keys can replace the old. Then it will be the attackers’ turn, and the game will continue.

It’s a game that inherently favors the attackers. In my experience, software analysts always beat the obfuscators, if the analysts are willing to work hard, as they are here. Every round of the game, the software authors will have to come up with new and unexpected tricks for restructuring their software – tricks that will have to resist the attackers’ ever-growing suite of analysis tools. And each time the attackers succeed, they’ll be able to decrypt all existing discs.

We can model the economic effect of this game. The key parameter is the attackers’ reaction time, that is, how long it takes the attackers to extract keys from each newly issued version of the player software. If this time is short – say, a few weeks – then the AACS authority won’t benefit much from playing this game, and the authority would be nearly as well off if it simply gave up and let the extracted keys remain valid and the exploited software stay in the field.

My guess is that the attackers will extract keys from the new software within about three weeks of its availability.

[Previous posts in this series: 1, 2, 3, 4, 5, 6, 7, 8.]

Alex wrote on Thursday about the next step in the breakdown of AACS, the encryption scheme used on next-gen DVD discs (HD-DVD and Blu-ray): last week a person named Arnezami discovered and published a processing key that apparently can be used to decrypt all existing discs.

We’ve been discussing AACS encryption, on and off, for several weeks now. To review the state of play: the encryption scheme serves two purposes: key distribution and traitor tracing. Key distribution ensures that every player device, except devices that have been blacklisted, can decrypt a disc. Traitor tracing helps the authorities track down which player has been compromised, if key information is leaked. The AACS authorities encode the header information for each disc in such a way that keys are distributed properly and traitor tracing can occur.

Or that’s the theory, at least. In practice, the authorities are making very little use of the traitor tracing facilities. We’re not sure why this is. They surely have an interest in tracing traitors, and failing to encode discs to facilitate traitor tracing is just a lost opportunity.

The main traitor tracing feature is the so-called sequence key mechanism. This mechanism is not used at all on any of the discs we have seen, nor have we seen any reports of its use.

A secondary traitor tracing feature involves the use of processing keys. Each player device has a unique set of a few hundred device keys, from which it can calculate a few billion different processing keys. Each processing key is computable by only a fraction of the players in the world. Each disc’s headers include a list of the processing keys that can decrypt the disc; any one of the listed processing keys is sufficient to decrypt the disc.

For some reason, all existing discs seem to list the same set of 512 processing keys. Each player will be able to compute exactly one of these processing keys. So when Arnezami leaked a processing key, the authorities could deduce that he must have extracted it from a player that knew that particular processing key. In other words, it narrowed down the identity of his player to about 0.2% of all possible players.

Because all existing discs use the same set of processing keys, the processing key leaked by Arnezami can decrypt any existing disc. Had the authorities used different sets of processing keys on different discs – which was perfectly feasible – then a single processing key would not have unlocked so many discs. Arnezami would have had to extract and publish many processing keys, which would have made his job more difficult, and would have further narrowed down which player he had.

The ability to use different processing key sets on different discs is part of the AACS traitor tracing facility. In failing to do this, the authorities once again failed to use the traitor tracing mechanisms at their disposal.

Why aren’t the authorities working as hard as they can to traitor-trace compromised players? Sure, the sequence key and processing key mechanisms are a bit complex, but if the authorities weren’t going to use these mechanisms, then why would they have gone to the difficulty and expense of designing them and requiring all players to implement them? It’s a mystery to us.

[Previous posts in this series: 1, 2, 3, 4, 5, 6, 7.]

This week brings further developments in the gradual meltdown of AACS (the encryption scheme used for HD-DVD and Blu-Ray discs). Last Sunday, a member of the Doom9 forum, writing under the pseudonym Arnezami, managed to extract a “processing key” from an HD-DVD player application. Arnezami says that this processing key can be used to decrypt all existing HD-DVD and Blu-Ray discs. Though currently this attack is more powerful than previous breaks, which focused on a different kind of key, its usefulness will probably diminish as AACS implementers adapt.

To explain what’s at stake, we need to describe a few more details about the way AACS manages keys. Recall that AACS player applications and devices are assigned secret device keys. Devices can use these keys to calculate a much larger set of keys called processing keys. Each AACS movie is encrypted with a unique title key, and several copies of the title key, encrypted with different processing keys, are stored on the disc. To play a disc, a device figures out which of the encrypted title keys it has the ability to decrypt. Then it uses its device keys to compute the necessary processing key, uses the processing key to decrypt the title key, and uses the title key to extract the content.

These three kinds of keys have different security properties that make them more or less valuable to attackers. Device keys are the most useful. If you know the device keys for a player, you can decrypt any disc that the player can. Title keys are the least useful, because each title key works only for a single movie. (Attacks on any of these keys will be limited by disc producers’ ability to blacklist compromised players. If they can determine which device has been compromised, they can change future discs so that the broken player, or its leaked device keys, won’t be able to decrypt them.)

To date, no device keys have been compromised. All successful breaks, before Arnezami, have involved extracting title keys from player software. These attacks are rather cumbersome–before non-technical users can decrypt a movie, somebody with the means to extract the title key needs to obtain a copy of the disc and publish its title key online. Multiple web sites for sharing title keys have been deployed, but these are susceptible to legal and technical threats.

So is the new attack on the processing key comparable to learning a venerable device key or a lowly title key? The answer is that, due to a strange quirk in the way the processing keys used on existing discs were selected, the key Arnezami published apparently can be used to decrypt every HD-DVD or Blu-Ray disc on the market. For the time being, knowing Arnezami’s processing key is as powerful as knowing a device key. For instance, someone could use the processing key to build a player or ripper that is able to treat all current discs as if they were unencrypted, without relying on online services or waiting for other users to extract title keys.

Yet this power will not last long. For future discs, processing key attacks will probably be no more valuable than title key attacks, working only on a single disc or a few discs at most. We’ll explain why in tomorrow’s post.

[Posts in this series: 1, 2, 3, 4, 5, 6, 7.]

By this point in our series on AACS (the encryption scheme used in HD-DVD and Blu-ray) it should be clear that AACS creates a nontrivial strategic game between the AACS central authority (representing the movie studios) and the attackers who want to defeat AACS. Today I want to sketch a model of this game and talk about who is likely to win.

First, let’s talk about what each party is trying to achieve. The central authority wants to maximize movie studio revenue. More precisely, they’re concerned with the portion of revenue that is due to AACS protection. We’ll call this the Marginal Value of Protection (MVP): the revenue they would get if AACS were impossible to defeat, minus the revenue they would get if AACS had no effect at all. The authority’s goal is to maximize the fraction of MVP that the studios can capture.

In practice, MVP might be negative. AACS makes a disc less useful to honest consumers, thereby reducing consumer demand for discs, which hurts studio revenue. (For example: Alex and I can’t play our own HD-DVD discs on our computers, because the AACS rules don’t like our computers’ video cards. The only way for us to watch these discs on our equipment would be to defeat AACS. (Being researchers, we want to analyze the discs rather than watch them, but normal people would insist on watching.)) If this revenue reduction outweighs any revenue increase due to frustrating infringement, MVP will be negative. But of course if MVP is negative then a rational studio will release its discs without AACS encryption; so we will assume for analytic purposes that MVP is positive.

We’ll assume there is a single attacker, or equivalently that multiple attackers coordinate their actions. The attacker’s motive is tricky to model but we’ll assume for now that the attacker is directly opposed to the authority, so the attacker wants to minimize the fraction of MVP that the studios can capture.

We’ll assume the studios release discs at a constant rate, and that the MVP from a disc is highest when the disc is first released and then declines exponentially, with time constant L. (That is, MVP for a disc is proportional to exp(-(t-t0)/L), where t0 is the disc’s release date.) Most of the MVP from a disc will be generated in the first L days after its release.

We’ll assume that the attacker can compromise a new player device every C days on average. We’ll model this as a Poisson process, so that the likelihood of compromising a new device is the same every day, or equivalently the time between compromises is exponentially distributed with mean C.

Whenever the attacker has a compromised device, he has the option of using that device to nullify the MVP from any set of existing discs. (He does this by ripping and redistributing the discs’ content or the keys needed to decrypt that content.) But once the attacker uses a compromised device this way, the authority gets the ability to blacklist that compromised device so that the attacker cannot use it to nullify MVP from any future discs.

Okay, we’ve written down the rules of the game. The next step – I’ll spare you the gory details – is to translate the rules into equations and solve the equations to find the optimal strategy for each side and the outcome of the game, that is, the fraction of MVP the studios will get, assuming both sides play optimally. The result will depend on two parameters: L, the commercial lifetime of a disc, and C, the time between player compromises.

It turns out that the attacker’s best strategy is to withhold any newly discovered compromise until a “release window” of size R has passed since the last time the authority blacklisted a player. (R depends in a complicated way on L and C.) Once the release window has passed, the attacker will use the compromise aggressively and the authority will then blacklist the compromised player, which essentially starts the game over. The studio collects revenue during the release window, and sometimes beyond the release window when the attacker gets unlucky and takes a long time to find another compromise.

The fraction of MVP collected by the studio turns out to be approximately C/(C+L). When C is much smaller than L, the studio loses most of the MVP, because the attacker compromises players frequently so the attacker will nullify a disc’s MVP early in the disc’s commercial lifetime. But when C is much bigger than L, a disc will be able to collect most of its MVP before the attacker can find a compromise.

To predict the game’s outcome, then, we need to know the ratio of C (the time needed to compromise a player) to L (the commercial lifetime of a disc). Unfortunately we don’t have good data to estimate C and L. My guess, though, is that C will be considerably less than L in the long run. I’d expect C to be measured in weeks and L in months. If that’s right, it’s bad news for AACS.